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Suppose I am fitting a logistic regression with intercept only, which is equivalent tho using the count to estimate the outcome probability and make prediction.

Can I say following?

We are using prior only to make the prediction.

I think some persons from CV corrected me, that the word prior has close relationship with Bayesian statistics, and the statement is not correct.

If it is not accurate, what should I say if we only use the counts to estimate the outcome probability?

Haitao Du
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    Try: We are using "counts" only to make the prediction" – Jon Aug 15 '16 at 18:28
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    Unless you're doing Bayesian Logistic regression, don't use the word prior. – Jon Aug 15 '16 at 18:29
  • If I read that, it would sound like a tautology. Of course in any Bayesian estimation a prior is used to make the posterior which is the prediction! Just don't use the word prior if it's not Bayesian. – Chris Rackauckas Aug 15 '16 at 18:36

2 Answers2

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I say it's fine.

Logistic regression estimates $P(Y = 1\vert X = x)$.

$$ P(Y = 1\vert X = x) = \dfrac{ P(X = x\vert Y = 1)P(Y = 1) }{ P(X = x) } $$

$P(Y = 1)$ is the prior probability that $Y = 1$.

If we only use an intercept in our model, no matter what features we have, then the probability predicted by the logistic regression model is the proportion of $Y$-values with $Y = 1$. This is $P(Y = 1)$, so the prior probability that $Y = 1$.

Dave
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Answered in comments by Jon:

Try: We are using "counts" only to make the prediction". Unless you're doing Bayesian Logistic regression, don't use the word prior.

mkt
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